Field of the Invention
The present invention relates to drive systems for electrostatic generators and motors, and more specifically, it relates to pulse-train drive systems for such circuits.
Description of Related Art
Electrostatic generator/motors, as described in the prior art, can be operated in either a generator or a motor mode. This invention describes an improved electronic drive system for applications requiring the motor mode. Such devices have application to flywheels for bulk energy storage, among myriad commercial and defense uses.
In general, electrostatic generator/motors involve the use of an assembly of rotating and stationary elements that together comprise a condenser (or, capacitor), the capacitance of which varies periodically with the motion of the rotating elements relative to the fixed elements. An example of the prior art is shown in FIG. 1A (top view) and in FIG. 1B (side view). Turning now to FIG. 1A, a circular array of fan-like stationary elements, 100, is depicted. Below this stationary array of elements is a similar circular array of elements, which is allowed to rotate about a vertical axis, referred to as the “rotor.” FIG. 1B shows a cross-sectional side view of the overall ES structure, showing an embodiment consisting of a set of two rotors, 106, with each respective rotor also comprised of a circular array of fan-like elements. Each respective rotor plate is bound on each circular surface by a stationary array of opposing, fan-like elements, 100, 104, and 102, respectively. The rotor plates are allowed to rotate about an axis oriented orthogonal to the plane of the fixed plate(s), as shown in FIG. 1A.
As shown in FIG. 1B, the rotors are comprised of a set of annular fan-like elements, with each element having a thickness greater than the basic substrate of the disc. In general, the thick fan-like sections elements of the rotor can consist of metallic (conductive) material, dielectric material or combinations thereof. Each pair of fixed fan-like elements, which comprises the opposing stationary plates, forms a capacitor of a fixed gap, g, in between which, each respective rotor traverses. As the moving discs rotate, the capacitance between each pair of opposing stationary plates will vary periodically, owing to differences in the gap dimension, g, and the properties of the rotor material, as each fan-like element of the rotor passes between each respective annular capacitor element in the array.
This structure can be configured either as an electrostatic (ES) generator or as an electrostatic (ES) motor, dependent on the details of an electrical circuit that includes this device. In the so-called “generator mode” of operation, rotation of the moving element results in the generation of an ac voltage arising from the basic equation for the voltage across a charged condenser when the capacitance varies with time, as indicated by Equation (1):
                              V          ⁡                      (            t            )                          =                              q                          C              ⁡                              (                t                )                                              ⁢                                          ⁢                      (            Volts            )                                              (        1        )            Here q (Coulombs) is the charge on the condenser and C(t) (Farads) is the time-varying value of the capacitance, the latter owing to the rotation of the element. If the capacitance varies periodically with time, then the ac output of the electrostatic generator will also be periodic, with an ac waveform that depends on the geometry of the time-varying condenser and on the charging circuitry that is employed.
The variable-capacity system described above is a “reciprocal” device, in that it is capable of functioning either as a generator or a motor, depending only on the circuitry to which it is attached. As a generator, an example of which is an energy storage flywheel, the generator output is high-frequency alternating current, which can easily be converted to mains-frequency power. As an example, the high-frequency generator output can be first rectified to dc, with the resultant dc output driving an electronic inverter to produce a 60 Hz output, the latter suitable for commercially powered devices.
By reciprocity, operation of the system in the so-called “motor mode” requires a drive circuitry that generates a pulse-like waveform, which is synchronized with the rotation frequency and phase of the rotating elements.
The physics principle here is exemplified by a simple example, as depicted in FIG. 2. Consider a 1-D parallel-plate capacitor of length L, comprised of a pair of stationary plates, 200 and 204, respectively, separated by a gap of dimension, g. Without loss of generality, assume that the system is fitted with a third plate, 206, also of length L. The third plate 206 is assumed to be a moveable metal (or dielectric) plate, which can be inserted between the pair of stationary plates, along the length of the capacitor, as shown in FIG. 2. This system results in a parallel-plate capacitor (the pair of fixed plates), whose value of the capacitance can be varied as the overlap, x, varies of the moveable plate relative to the fixed parallel plates. In general, as the overlap, x, of the plates increases, there is a concomitant increase in the value of the overall device capacitance.
Consider the case where, initially, there is no overlap of the moveable plate relative to the pair of stationary plates (x=0). That is, all three plates are parallel to each other; however, the central plate, 206, is laterally displaced to the left, by a distance, L, relative to the pair of (overlapping) stationary plates, 200 and 204. In other words, the central plate is initially positioned to be completely outside the gap between the two fixed plates.
Assume now that an external potential, 210, of magnitude V0, is applied across the two stationary plates. Under this condition, as the leading edge of the moveable plate enters the gap between them (i.e., x>0), the moveable plate will be subject to an attractive electrostatic force, FES, that will persist until the plate 206 has reached the point whereby the capacitance of the capacitor is a maximum (x=L). If the plate is moved beyond this maximal point (x>L), so that the capacitance begins to decrease, the direction of the attractive force, FES, will reverse and then approach zero again as the plate emerges from the far side of the capacitor (x>2L).
To optimally apply this electrostatic force on the moveable plate to produce motor action in the same direction, it is necessary to ensure that the driving voltage be turned off during those times when the capacity is decreasing, and vice versa.
In other words, the driving voltage is to be switched “on” as the plate moves forward and enters the gap (x>0)—during which time, the electrostatic force, FES, is attractive—further drawing the plate into the gap. Then, as the moveable plate begins to emerge from the gap (x>L)—during which time the attractive force would have otherwise changed direction—the driving force is switched “off,” enabling the plate to continue its forward propagation through the gap (x>L), without any applied force to retard its trajectory.
The physics of the linear device shown in FIG. 2 can be extended to that of a device with circular symmetry, in the context of the ES motor geometry. Turning now to FIG. 3 and FIG. 4, an analogous set of conditions apply. FIG. 3 depicts a top view of an ES motor, and, FIG. 4 shows a cross sectional drawing of the same, along the A-A′ cut.
In the example shown in FIG. 3 and FIG. 4, the ES motor consists of two stationary plates, 300 and 304, separated by a fixed distance (or, gap), g, each with a respective set of fixed elements, arranged in an annular pattern. Between these two discs, a rotating plate, 306, is positioned, with a corresponding set of thick fan-like elements, each of which is comprised of conductive and/or dielectric materials. For ease of viewing, the cross-sectional view, A-A′, in FIG. 4 depicts a rotor with only a single pair of diametrically opposed thick elements. As the rotor revolves, the capacitance between the stationary plates, 300 and 304, as formed by opposing pairs of the fixed fan-like sections, will vary periodically.
The basic operation of the circular device, in terms of its periodically varying capacitance during operation, can be appreciated by viewing an annular cross section B-B′, depicted by the dashed arc in FIG. 3 and, also, by the cross-sectional cut, also labeled as B-B′, in FIG. 4. The linear representation of the varying capacitance, as discussed with respect to FIG. 2, provides a good approximation of the salient details that underlie the operation of the circular ES device. Under this approximation, the “arc-axes,” labeled by “x” in FIG. 3, are analogous to the linear x-axis shown in FIG. 2. In essence, therefore, the view seen in FIG. 2 is essentially equivalent to the B-B′ cross-sectional cut depicted in FIG. 3.
Returning now to FIG. 3, upon the application of a voltage across the pair of fixed capacitor plates, 300 and 304, the thick segments along the rotating plate, 306, will each experience a tangential electrostatic force, FES, in the direction of the stator plates, resulting in a rotation of the rotor in the direction of this force. The rotor will revolve about its axis so that its thick segments will be attracted into the respective regions between the pair of opposing fixed-plate segments, in complete analogy to the linear representation shown in FIG. 2. Upon complete overlap of the rotor segments 306 with the respective segments of the fixed plates, the voltage across the fixed plates 300 and 304 is switched off, so that the rotor continues to freely rotate in the same direction, without any counteracting tangential force. Therefore, the rotor will continue to rotate in the same sense, until it approaches the stationary plates of a subsequent pair of opposing fixed elements. In the case of a rotor with a single-segmented device, this condition will occur after a single revolution. In analogy to motors in general, the IS motor can be scaled so that the rotor and stator consist of more than a single element. Hence, in the case of a multi-segmented device, the condition of subsequent overlap will occur after rotation by an angle of 360°/2n, where n is equal to the number of segments about the annular circumference of the device. In general, at the point of subsequent overlap of the rotor element with that of the stationary pair of elements, the voltage is again switched on, resulting in an attractive tangential force, and, the process repeats. Thus, by proper synchronization and application of the time-dependent attractive force, continuous angular rotation in one direction is realized, thereby resulting in an electrostatic motor.